Preisach-model-based position control of a shape-memory alloy linear actuator in the presence of time-varying stress

Tensioned shape-memory alloy (SMA) wires can repeatedly contract and extend, according to hysteretic loops defined by the shape-memory effect (SME), when subject to cyclic heating and cooling. Empirical evidence shows that these periodic hysteretic deformations are also a function of the loading stress applied to the tested wire. Therefore, to achieve accurate position control of an SMA wire-actuator, the SME hysteretic phenomenon in the presence of time-varying loading stress must be explicitly modeled in order to be compensated. To this end, we use a Preisach-model-based forward mapping that relates the time-varying exciting temperature and stress signals as inputs with the produced strain signal as the output, and whose parameters are experimentally estimated a priori through a series of steps in a nonlinear system identification process. Then, the identified parameters are employed by a Preisach-model-based inversion algorithm that is integrated into a feedforward inverse control scheme designed to mitigate the effects of hysteresis affecting the tested SMA wire. In the proposed scheme, the inverse controller reads two time-varying inputs, a strain reference and the known stress signal exciting the controlled SMA wire-actuator, and then it computes the corresponding temperature reference that, once enforced on the SMA material of the wire, generates the desired strain output. This approach to position tracking control can be realized using lightweight sensors and, as demonstrated in this paper through experimental results, is computationally efficient, which are the two most essential features required for the implementation of controllers on centimeter-scale autonomous robots. Using data obtained through real-time experiments, we demonstrate that the introduced position control scheme is highly effective and suitable to be used in future microrobotic applications. Furthermore, we show that the proposed methods for the system identification of the nonlinear hysteretic dynamics of SMA wires and for the synthesis of inverse controllers can be easily modified to be applied to the tracking control of SMA actuators thermally excited by means other than Joule heating.